메뉴 건너뛰기




Volumn 9, Issue 4, 2008, Pages 1714-1726

A delayed epidemic model with stage-structure and pulses for pest management strategy

Author keywords

Attractivity; Delay; Impulsive control; Permanence; Pest management; Stage structure

Indexed keywords

DYNAMICAL SYSTEMS; EPIDEMIOLOGY; NONLINEAR ANALYSIS; STROBOSCOPES; TIME DELAY;

EID: 43649101953     PISSN: 14681218     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.nonrwa.2007.05.004     Document Type: Article
Times cited : (201)

References (47)
  • 1
    • 0025132577 scopus 로고
    • A time delay model of single species growth with stage structure
    • Aiello W.G., and Freedman H.I. A time delay model of single species growth with stage structure. Math. Biosci. 101 (1990) 139-156
    • (1990) Math. Biosci. , vol.101 , pp. 139-156
    • Aiello, W.G.1    Freedman, H.I.2
  • 2
    • 0000675649 scopus 로고
    • Regulation and stability of host-parasite population interactions, I: regulatory processes
    • Anderson R.M., and May R.M. Regulation and stability of host-parasite population interactions, I: regulatory processes. J. Anim. Ecol. 47 (1978) 219-247
    • (1978) J. Anim. Ecol. , vol.47 , pp. 219-247
    • Anderson, R.M.1    May, R.M.2
  • 4
    • 0024900429 scopus 로고
    • Space limited recruitment in open systems: the importance of time delays
    • Bence J.B., and Nisbet R.M. Space limited recruitment in open systems: the importance of time delays. Ecology 70 (1989) 1434-1441
    • (1989) Ecology , vol.70 , pp. 1434-1441
    • Bence, J.B.1    Nisbet, R.M.2
  • 5
    • 43649097042 scopus 로고    scopus 로고
    • Smooth dependence by lag of the solution of a delay integro-differential equation from biomathematics
    • Bica A.M., and Muresan S. Smooth dependence by lag of the solution of a delay integro-differential equation from biomathematics. Commun. Math. Anal. 1 (2006) 64-74
    • (2006) Commun. Math. Anal. , vol.1 , pp. 64-74
    • Bica, A.M.1    Muresan, S.2
  • 6
    • 0000756289 scopus 로고    scopus 로고
    • Behaviour of solutions to Marchuk's model depending on a time delay
    • Bodnar M., Forys U., and Urszula. Behaviour of solutions to Marchuk's model depending on a time delay. Int. J. Appl. Math. Comput. Sci. 10 (2000) 97-112
    • (2000) Int. J. Appl. Math. Comput. Sci. , vol.10 , pp. 97-112
    • Bodnar, M.1    Forys, U.2    Urszula3
  • 7
    • 0842337246 scopus 로고    scopus 로고
    • Pathogen incidence and their potential as microbial control agents in IPM of maize stemborers in West Africa
    • Cherry A.J., Lomer C.J., Djegui D., and Schulthess F. Pathogen incidence and their potential as microbial control agents in IPM of maize stemborers in West Africa. Biocontrol 44 (1999) 301-327
    • (1999) Biocontrol , vol.44 , pp. 301-327
    • Cherry, A.J.1    Lomer, C.J.2    Djegui, D.3    Schulthess, F.4
  • 8
    • 0012099291 scopus 로고    scopus 로고
    • The effect of dispersal on population growth with stage-structure
    • Cui J.A., Chen L.S., and Wang W.D. The effect of dispersal on population growth with stage-structure. Comput. Math. Appl. 39 (2000) 91-102
    • (2000) Comput. Math. Appl. , vol.39 , pp. 91-102
    • Cui, J.A.1    Chen, L.S.2    Wang, W.D.3
  • 12
    • 18144413585 scopus 로고    scopus 로고
    • On pulse vaccination strategy in the SIR epidemic model with vertical transmission
    • d'Onofrio A. On pulse vaccination strategy in the SIR epidemic model with vertical transmission. Appl. Math. Lett. 18 (2005) 729-732
    • (2005) Appl. Math. Lett. , vol.18 , pp. 729-732
    • d'Onofrio, A.1
  • 13
    • 0003033405 scopus 로고
    • Pest control using the fungi Beauveria and Metarhizinm
    • Burges H.D. (Ed), Academic Press, London
    • Ferron P. Pest control using the fungi Beauveria and Metarhizinm. In: Burges H.D. (Ed). Microbial Control in Pests and Plant Diseases (1981), Academic Press, London
    • (1981) Microbial Control in Pests and Plant Diseases
    • Ferron, P.1
  • 14
    • 0009976576 scopus 로고    scopus 로고
    • A contribution to the study of functional differential equations with impulses
    • Franco D., Liz E., Nieto J.J., and Rogovchenko Y.V. A contribution to the study of functional differential equations with impulses. Math Nachr. 218 (2000) 49-60
    • (2000) Math Nachr. , vol.218 , pp. 49-60
    • Franco, D.1    Liz, E.2    Nieto, J.J.3    Rogovchenko, Y.V.4
  • 15
    • 0017142168 scopus 로고
    • Graphical stability, enrichment, and pest control by a natural enemy
    • Freedman H.I. Graphical stability, enrichment, and pest control by a natural enemy. Math. Biosci. 31 (1976) 207-225
    • (1976) Math. Biosci. , vol.31 , pp. 207-225
    • Freedman, H.I.1
  • 16
    • 0027706230 scopus 로고
    • Invasion and chaos in a periodically pulsed mass-action chemostat
    • Funasaki E., and Kot M. Invasion and chaos in a periodically pulsed mass-action chemostat. Theor. Pop. Biol. 44 (1994) 203-224
    • (1994) Theor. Pop. Biol. , vol.44 , pp. 203-224
    • Funasaki, E.1    Kot, M.2
  • 17
    • 33746833233 scopus 로고    scopus 로고
    • Analysis of a delayed epidemic model with pulse vaccination and saturation incidence
    • Gao S.J., Chen L.S., Nieto J.J., and Torres A. Analysis of a delayed epidemic model with pulse vaccination and saturation incidence. Vaccine 24 (2006) 6037-6045
    • (2006) Vaccine , vol.24 , pp. 6037-6045
    • Gao, S.J.1    Chen, L.S.2    Nieto, J.J.3    Torres, A.4
  • 19
    • 0035108340 scopus 로고    scopus 로고
    • A two-component model of host-parasitoid interactions: determination of the size of inundative releases of parasitoids in biological pest control
    • Grasman J., Van Herwarrden O.A., Hemerik L., et al. A two-component model of host-parasitoid interactions: determination of the size of inundative releases of parasitoids in biological pest control. Math. Biosci. 196 (2001) 207-216
    • (2001) Math. Biosci. , vol.196 , pp. 207-216
    • Grasman, J.1    Van Herwarrden, O.A.2    Hemerik, L.3
  • 21
    • 2942631566 scopus 로고    scopus 로고
    • Impulsive vaccination of SIR epidemic models with nonlinear incidence rates
    • Hui J., and Chen L.S. Impulsive vaccination of SIR epidemic models with nonlinear incidence rates. Discrete Continuous Dynamical Syst. Ser. B 3 (2004) 595-606
    • (2004) Discrete Continuous Dynamical Syst. Ser. B , vol.3 , pp. 595-606
    • Hui, J.1    Chen, L.S.2
  • 22
    • 34547319856 scopus 로고    scopus 로고
    • Impulsive ecological control of staged-structured pest management system
    • Jiang G.R., Lu Q.S., and Peng L.P. Impulsive ecological control of staged-structured pest management system. Math. Biosci. Eng. 2 (2005) 329-344
    • (2005) Math. Biosci. Eng. , vol.2 , pp. 329-344
    • Jiang, G.R.1    Lu, Q.S.2    Peng, L.P.3
  • 23
    • 0347269498 scopus 로고    scopus 로고
    • Bifurcation of nontrivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment
    • Lakmeche A., and Arino O. Bifurcation of nontrivial periodic solutions of impulsive differential equations arising chemotherapeutic treatment. Dynamics of Continuous, Discrete Impulsive Syst. 7 (2000) 265-287
    • (2000) Dynamics of Continuous, Discrete Impulsive Syst. , vol.7 , pp. 265-287
    • Lakmeche, A.1    Arino, O.2
  • 25
    • 33746901580 scopus 로고    scopus 로고
    • A new existence theory for positive periodic solutions to functional differential equations with impulse effects
    • Li X., Zhang X., and Jiang D. A new existence theory for positive periodic solutions to functional differential equations with impulse effects. Comput. Math. Appl. 51 (2006) 1761-1772
    • (2006) Comput. Math. Appl. , vol.51 , pp. 1761-1772
    • Li, X.1    Zhang, X.2    Jiang, D.3
  • 26
    • 27144533856 scopus 로고    scopus 로고
    • The dynamics of a prey-dependent consumption model concerning impulsive control strategy
    • Liu B., Chen L.S., and Zhang Y.J. The dynamics of a prey-dependent consumption model concerning impulsive control strategy. Appl. Math. Comput. 169 (2005) 305-320
    • (2005) Appl. Math. Comput. , vol.169 , pp. 305-320
    • Liu, B.1    Chen, L.S.2    Zhang, Y.J.3
  • 27
    • 33750615413 scopus 로고    scopus 로고
    • Existence of positive periodic solutions for neutral functional differential equations
    • Liu G., Yan J., and Zhang F. Existence of positive periodic solutions for neutral functional differential equations. Nonlinear Anal. 66 (2007) 253-267
    • (2007) Nonlinear Anal. , vol.66 , pp. 253-267
    • Liu, G.1    Yan, J.2    Zhang, F.3
  • 28
    • 0037032855 scopus 로고    scopus 로고
    • Recent progress on stage-structured population dynamics
    • Liu S.Q., Chen L.S., and Agarwal R. Recent progress on stage-structured population dynamics. Math. Comput. Model 36 (2002) 1319-1360
    • (2002) Math. Comput. Model , vol.36 , pp. 1319-1360
    • Liu, S.Q.1    Chen, L.S.2    Agarwal, R.3
  • 29
    • 0037332898 scopus 로고    scopus 로고
    • Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator
    • Liu X.N., and Chen L.S. Complex dynamics of Holling type II Lotka-Volterra predator-prey system with impulsive perturbations on the predator. Chaos Solitons Fractals 16 (2003) 311-320
    • (2003) Chaos Solitons Fractals , vol.16 , pp. 311-320
    • Liu, X.N.1    Chen, L.S.2
  • 30
    • 0000366981 scopus 로고
    • Impulsive stabilization and applications to population growth models
    • Liu X.Z. Impulsive stabilization and applications to population growth models. J. Math. 25 1 (1995) 381-395
    • (1995) J. Math. , vol.25 , Issue.1 , pp. 381-395
    • Liu, X.Z.1
  • 31
    • 0032165830 scopus 로고    scopus 로고
    • Impulsive control of a Lotka-Volterra system
    • Liu X.Z., and Rohof K. Impulsive control of a Lotka-Volterra system. IMA J. Math. Control Inf. 15 (1998) 269-284
    • (1998) IMA J. Math. Control Inf. , vol.15 , pp. 269-284
    • Liu, X.Z.1    Rohof, K.2
  • 32
    • 33750837966 scopus 로고    scopus 로고
    • Further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations
    • Liu Y. Further results on periodic boundary value problems for nonlinear first order impulsive functional differential equations. J. Math. Anal. Appl. 327 (2007) 435-452
    • (2007) J. Math. Anal. Appl. , vol.327 , pp. 435-452
    • Liu, Y.1
  • 33
    • 0021039638 scopus 로고
    • The potential of predators for pest control
    • Luff M.L. The potential of predators for pest control. Agr. Ecosyst. Environ. 10 (1983) 159-181
    • (1983) Agr. Ecosyst. Environ. , vol.10 , pp. 159-181
    • Luff, M.L.1
  • 34
    • 18844464485 scopus 로고    scopus 로고
    • Destabilizing effect of cannibalism on a structured predator-prey system
    • Magnusson K.G. Destabilizing effect of cannibalism on a structured predator-prey system. Math. Biosci. 155 (1999) 61-75
    • (1999) Math. Biosci. , vol.155 , pp. 61-75
    • Magnusson, K.G.1
  • 35
    • 33645079919 scopus 로고    scopus 로고
    • Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations
    • Nieto J.J., and Rodriguez-Lopez R. Periodic boundary value problem for non-Lipschitzian impulsive functional differential equations. J. Math. Anal. Appl. 318 (2006) 593-610
    • (2006) J. Math. Anal. Appl. , vol.318 , pp. 593-610
    • Nieto, J.J.1    Rodriguez-Lopez, R.2
  • 36
    • 0032213158 scopus 로고    scopus 로고
    • Pulse vaccination strategy in the SIR epidemic model
    • Shulgin B., Stone L., and Agur Z. Pulse vaccination strategy in the SIR epidemic model. Bull. Math. Biol. 60 (1998) 1123-1148
    • (1998) Bull. Math. Biol. , vol.60 , pp. 1123-1148
    • Shulgin, B.1    Stone, L.2    Agur, Z.3
  • 37
    • 0023967009 scopus 로고    scopus 로고
    • Systems of ordinary differential equations which generate an order preserving flow
    • Smith H.L. Systems of ordinary differential equations which generate an order preserving flow. SIAM Rev. 30 (1998) 87-98
    • (1998) SIAM Rev. , vol.30 , pp. 87-98
    • Smith, H.L.1
  • 38
    • 0036483349 scopus 로고    scopus 로고
    • Density-dependent birth rate, birth pulses and their population dynamic consequences
    • Tang S.Y., and Chen L.S. Density-dependent birth rate, birth pulses and their population dynamic consequences. J. Math. Biol. 44 (2002) 185-199
    • (2002) J. Math. Biol. , vol.44 , pp. 185-199
    • Tang, S.Y.1    Chen, L.S.2
  • 39
    • 36749052819 scopus 로고    scopus 로고
    • X.H. Tang, Z. Jiang, Periodic solutions of first-order nonlinear functional differential equations, Nonlinear Anal, in press, doi: 10.1016/j.na.2006.11.041.
    • X.H. Tang, Z. Jiang, Periodic solutions of first-order nonlinear functional differential equations, Nonlinear Anal, in press, doi: 10.1016/j.na.2006.11.041.
  • 40
    • 0002986807 scopus 로고    scopus 로고
    • Measures of success in biological control of anthropoids by augmentation of natural enemies
    • Wratten S., and Gurr G. (Eds), Kluwer Academic Publishers, Dordrdcht
    • Van Lenteren J.C. Measures of success in biological control of anthropoids by augmentation of natural enemies. In: Wratten S., and Gurr G. (Eds). Measures of Success in Biological Control (2000), Kluwer Academic Publishers, Dordrdcht
    • (2000) Measures of Success in Biological Control
    • Van Lenteren, J.C.1
  • 41
    • 0031124171 scopus 로고    scopus 로고
    • A predator-prey system with stage-structure for predator
    • Wang W.D., and Chen L.S. A predator-prey system with stage-structure for predator. Comp. Math. Appl. 33 (1997) 83-91
    • (1997) Comp. Math. Appl. , vol.33 , pp. 83-91
    • Wang, W.D.1    Chen, L.S.2
  • 42
    • 33846591097 scopus 로고    scopus 로고
    • Global stability of a predator-prey system with stage structure for the predator
    • Xiao Y.N., and Chen L.S. Global stability of a predator-prey system with stage structure for the predator. Acta Math. Sin. Engl. Ser. 19 (2003) 1-11
    • (2003) Acta Math. Sin. Engl. Ser. , vol.19 , pp. 1-11
    • Xiao, Y.N.1    Chen, L.S.2
  • 43
    • 12944265108 scopus 로고    scopus 로고
    • Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka-Volterra systems
    • Yan J.R., Zhao A., and Nieto J.J. Existence and global attractivity of positive periodic solution of periodic single-species impulsive Lotka-Volterra systems. Math. Comput. Model 40 (2004) 509-518
    • (2004) Math. Comput. Model , vol.40 , pp. 509-518
    • Yan, J.R.1    Zhao, A.2    Nieto, J.J.3
  • 44
    • 34548398149 scopus 로고    scopus 로고
    • H. Zhang, L.S. Chen, Pest Management Through Continuous and Impulsive Control Strategies, Biosystems, in press, doi: 10.1016/j.biosystems.2006.09.038.
    • H. Zhang, L.S. Chen, Pest Management Through Continuous and Impulsive Control Strategies, Biosystems, in press, doi: 10.1016/j.biosystems.2006.09.038.
  • 45
    • 27144526577 scopus 로고    scopus 로고
    • Chaos in periodically forced Holling type II predator-prey system with impulsive perturbations
    • Zhang S.W., Tan D.J., and Chen L.S. Chaos in periodically forced Holling type II predator-prey system with impulsive perturbations. Chaos Solitons Fractals 28 (2006) 367-376
    • (2006) Chaos Solitons Fractals , vol.28 , pp. 367-376
    • Zhang, S.W.1    Tan, D.J.2    Chen, L.S.3
  • 46
    • 1942489227 scopus 로고    scopus 로고
    • Periodicity in a generalized ecological competition system governed by impulsive differential equations with delays
    • Zhang W., and Fan M. Periodicity in a generalized ecological competition system governed by impulsive differential equations with delays. Math. Comput. Model 39 (2004) 479-493
    • (2004) Math. Comput. Model , vol.39 , pp. 479-493
    • Zhang, W.1    Fan, M.2
  • 47
    • 2942669677 scopus 로고    scopus 로고
    • The stage-structure predator-prey model and optimal harvesting policy
    • Zhang X., Chen L.S., and Neuman A.U. The stage-structure predator-prey model and optimal harvesting policy. Math. Biosci. 101 (2000) 139-153
    • (2000) Math. Biosci. , vol.101 , pp. 139-153
    • Zhang, X.1    Chen, L.S.2    Neuman, A.U.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.